含耗散函数的拉格朗日方程及耗散函数的物理意义

分析力学的拉格朗日方程是机械振动理论的基础，含耗散函数的拉格朗日方程又是这个基础的重要方面，本文作者首先定义出耗散函数，由耗散函数导出广义耗散力，然后建立含耗散函数的拉格朗日方程；最后讨论耗散涵数的物理意义，本文讨论的耗散力是指粘滞阻力，可视为线性阻力，因此含耗散函数的拉格朗日方程及由此建立的振动微分方程被日益广泛地应用于工程实践中去。

The Lagrange's equation containing dissipation function and the physical meaning of such functions

Lagrange's equation in analytical mechanics is the basis of the mechanical vibration theory and the equation with dissipation function is important to this basis.The author provides a definition of the dissipation function from which the generalized dissipation force is derived.The Lagrange's equation containing dissipation function is then established and finally the physical significance of dissipation function is discussed.The dissipation force discussed in the paper refers to the viscosity resistance which can be considered as one type of linear resistance,therefore,the Lagrange's equation containing dissipation function and the vibration differentiating equation derived from it can be applied widely to engineering practice.